To make crew socks, I knit thirty rounds of k2p2 ribbing on #0 needles, thirty rounds on #00, and thirty rounds on #000, then knit the foot. (This is my "mindless knitting", to work when my mind is on something else.) The stiffness of the ribbing holds crew socks up.
To make knee socks, measure yourself just under the knee, at the fullest part of the calf, and at the narrowest part of the ankle. Also measure the vertical distances between these measurements, and notice how wide the fullest and narrowest parts are.
Cast on enough stitches to go around under your knee. (If you don't think this measurement will stretch over your calf, you can make it a bit loose -- the top of the stocking will be drawn in by the garter.) Use a cast-on that will make it easy to pick up stitches to knit the cuff when the stocking is finished. I prefer a provisional cast on to an invisible cast on: the string stitches protect the live stitches while you are working, and you don't have a bunch of holders or a cable needle getting in your way.
Increase at a rate that will give you the correct number of stitches to go around the calf when you get there. The easiest way to shape is to increase or decrease on both sides of a "seam" stitch worked in purl or marked some other way -- in an aran sock, for example, you could have a cable or a twisted-stitch ridge running down the center back. In stranded knitting, you can use a vertical stripe to mark the "seam".
When you have two or three inches done, measure the actual knitting and re-calculate if it differs from your swatch. Keep careful notes, or use two sets of needles and keep both socks in the same stage of development.
When you've increased to the calf measurement, work straight for at least an inch (more if your calf-curve isn't sharp), then decrease at a rate that will give you the correct number of stitches for the ankle when you get there. Plan to hit the final number at least one inch before the full length; many legs are straight for two or three inches at the ankle.
If the sock yarn is all wool, don't sweat the details too much; I've made ghastly errors in shaping and still got wearable socks because wool is so forgiving.
Make the heel by any method you like. The only point to observe is that the center of the heel must line up with the center back of the leg.
(I like the flap heel because it allows me to use a thicker stitch where the shoe rubs. If the heel stitch draws in, work the first row with two yarns worked alternately. Work enough of the stitches with both yarns to widen the flap enough to make up for the drawing-in. (Sit in a good light when working the following row, as two stitches worked into one stitch tend to look like one stitch.) Using two yarns thickens the work enough, so knit (or purl) the increase row plain.)
When the foot is finished, put the socks on. They will be stretched from being pulled on, so walk around until they start to fall down, then pat them into place so you can see how much too short they are. If they aren't too short, knit on a cuff to turn down.
If they are too short, measure the distance carefully, then pick up the live stitches and work enough rounds of k1p1 ribbing to make up the difference. Then work three rounds of plain knitting (one round if the yarn is coarse), which will curl to the outside and cause your cuff to flop down neatly. Work in any non-curling pattern you please until the cuff is at least two inches wide, then use any non-constricting bind off. (I like Medrith Glover's pointed border.) The wider the cuff is, the more reliably it stays turned down.
If your cuff pattern looks better with the other side out, make a short-row turn just before starting it, or pick up the live stitches on the inside of the sock and purl the turning welt instead of knitting it.
Cut two pieces of cord elastic long enough to go around your leg comfortably and tie the ends together. Put these garters on over the socks and turn the cuffs down to hide them. (In ancient times one tied a ribbon around the leg to hold up the stockings, hence the custom of decorating the garter with a ribbon "flash" when wearing kilt hose.)
Lecture on how to calculate the in/decreases will be posted on request.
The feet of socks last longer if knitted very tight from worsted-spun (combed) wool.
Multiple strands of DMC Medici crewel yarn make nice flat darns.
Joy Beeson